This proposal aims at the development of mathematical, computer, recombinant DNA, selection and screening procedures to attain adaptive evolution of entirely novel peptides or fusion proteins with useful catalytic, ligand binding, structural or other features. Potential uses range from industrial catalysis to production of new drugs and vaccines. We have at present generated about 10,000,000,000 novel genes cloned into lambda- gtll, and appear to have successfully identified novel fusion peptides conferring gentamycin resistance to host bacteria. Mathematical work includes development of theory about the character of "adaptive walks" in the space of possible peptides, via point mutations or recombination, to peptides which are local or global optima for a desired function. We shall complete current work characterizing different novel peptides which as fusion proteins confer resistance to gentamycin in E. Coli lysogens. We will then test the relative efficiency of point mutants versus recombination in adaptive hill climbing. In addition we shall select for novel peptides or fusion proteins with a desired catalytic function. Notably we will select for beta- galactosidase function, and triosephosphate isomerase function in appropriate bacterial deletion mutants. A broad purpose of our efforts is to obtain novel peptides which can mimic the biological effects of almost arbitrary signal molecules such as hormones, growth factors, even pathogenic antigens. The central idea is simple: screen or select for novel peptides which are bound by a shape complement of the target molecule. The shape complement might be a receptor for a growth factor, or an antibody against the growth factor. As an initial example, we shall screen for epidermal growth factor (EGF) mimetic peptides which cross react to antibodies against the EGF target molecule. In addition we shall develop a general procedure to select for novel peptides mimicing arbitrary epitopes. Such mimetic peptides may be useful as drugs or vaccines. The fundamental importance of this work includes analysis of the distribution of function in peptide space and opening the way towards a technology of applied molecular evolution.